Scheme of Work – Mathematics stage 4
Introduction
This document is a scheme of work created by Cambridge as a suggested plan of delivery for Cambridge Primary Mathematics stage 4. Learning objectives for
the stage have been grouped into topic areas or ‘Units’. These have then been arranged in a recommended teaching order but you are free to teach objectives in
any order within a stage as your local requirements and resources dictate.
The scheme for Mathematics has assumed a term length of 10 weeks, with three terms per stage and three units per term. An overview of the sequence, number
and title of each unit for stage 4 can be seen in the table below.
The scheme has been based on the minimum length of a school year to allow flexibility. You should be able to add in more teaching time as necessary, to suit the
pace of your learners and to fit the work comfortably into your own term times.
Problem solving learning objectives are recurring, appearing in every unit. Activities and resources are suggested against the learning objectives to illustrate
possible methods of delivery.
There is no obligation to follow the published Cambridge Scheme of Work in order to deliver Cambridge Primary. It has been created solely to provide an
illustration of how delivery might be planned over the six stages.
A step-by-step guide to creating your own scheme of work and implementing Cambridge Primary in your school can be found in the Cambridge Primary Teacher
Guide available on the Cambridge Primary website. Blank templates are also available on the Cambridge Primary website for you to use if you wish.
Overview
Term 1
Term 2
Term 3
1A Number and Problem Solving
2A Number and Problem Solving
3A Number and Problem Solving
1B Measure and Problem Solving
2B Geometry and Problem Solving
3B Measure and Problem Solving
1C Handling data and Problem Solving
2C Measure and Problem Solving
3C Handling data and Problem Solving
V1 1Y07
Mathematics Stage 4
1
Scheme of Work – Mathematics stage 4
Unit 1A: Number and Problem Solving
Framework
Codes
Learning Objective
Activities
Resources
Comments
Numbers and the number system
4Nn1
Read and write number up to
10000.
Respond to oral and written questions
and statements such as: What is this
number? Write this number.
Number cards, large 100
square, large number line.
4Nn2
Count on and back in ones, tens,
hundreds and thousands from four
digit numbers.
Respond to oral questions at the start
of the lesson.
100 grid, place value cards.
4Nn3
Understand what each digit
represents in a three or four digit
number and partition into
thousands, hundreds, tens and
units.
Respond to oral or written questions
and statements such as ‘What does the
digit 7 mean in 472?’
‘What number needs to go in each box?
Explain why. * + 300 + 20 + 1 = 4321
Place value cards, large class
set and a set per pupil.
4Nn8
Recognise the multiples of 5, 10
and 100 up to 1000.
Using 100 square. Look, see and say.
Make your calculation:
Make and complete as many numbers
sentences as they can using the given
cards.
100 square; number cards of
multiples of 5, 10, 100 up to
1000; number cards 1 -10; x
and = cards
4Nn9
Round 3 and 4 digit numbers to the
nearest 10 or 100.
Go shopping!
Buying items and finding approximate
totals by rounding prices to nearest
dollar.
Mathematics Stage 4
Price tags, sheet of labels to
cut out.
V1 1Y07
Needs advanced
preparation.
2
Framework
Codes
Learning Objective
Activities
Resources
Comments
4Nn10
Position accurately numbers up to
1000 on an empty number line or
line marked off in multiples of 10 or
100.
Play games with marked dice to
generate 2, 3 or 4 digit numbers.
Dice; number line marked in
multiples of 10 or 100
Number lines may
need to be prepared
4Nn11
Estimate where 3 and 4 digit
numbers lie on an empty 0 – 1000.
Student activity: A group of students
each have a 2, 3 or 4 digit number. The
rest of the class instruct the group so
that they stand smallest to largest
number on an imaginary number line.
Take the activity to table top.
Large numbers of 2, 3 or 4
digit numbers; empty number
line 0 – 1000.
Number lines may
need to be prepared.
4Nn12
Compare pairs of 3 or 4 digit
numbers, using the < and > signs
and find a number in-between each
pair.
Filling a base board. Piles of cards (<
and >, and 0-9 digit cards) are placed
face down. The top card of each pile is
turned over and placed on the grid to
make a number statement. Is it true?
2 Base boards marked H. T.
U.;
< and > cards; digit cards 0 –
9
Base boards and cards
need to be prepared
Calculation
Mental strategies
4Nc5
Recognise and begin to know
multiples of 2, 3, 4, 5 and 10 up to
the tenth multiple.
Respond to written or oral questions.
Multiplication grid.
4Nc6
Add 3 or 4 small numbers, finding
pairs that equal 10 or 20.
Using a dartboard: Make a simple
dartboard circle with 6 segments each
numbered with a single digit. Using 3 or
4 ‘darts’ how many ways can a total of
10 or 20 be made?
Dartboard; paper ‘darts’; sticky
plastic.
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Mathematics Stage 4
Dartboard needs to be
prepared.
3
Framework
Codes
Learning Objective
Activities
Resources
4Nc9
Add any pair of 2 digit numbers,
choosing an appropriate strategy.
Use dice to generate 2 digit numbers.
Encourage different strategies.
Numbered dice.
4Nc10
Subtract any pair of 2 digit
numbers, choosing an appropriate
strategy.
Use dice to generate 2digit numbers.
Subtract one for the other using
appropriate strategy
Numbered dice.
4Nc13
Multiply any pair of single digit
numbers together.
Respond to questions orally.
4Nc14
Use knowledge of commutativity to
find the easier way to multiply.
Understand and use the idea of the
commutative law (3 x 43 = 43 x 3).
Use dice to generate 1 and 2 digit
numbers.
Numbered dice.
4Nc15
Understand the effect of multiplying
and dividing 3 digit numbers by 10.
Calculator activity: Put in any multiple of
10. Press the divide key and then 10.
Press =. What do you notice? Put in
any number, x by 10. Press =. What do
you notice?
Calculator.
Comments
Some students may
need extra practice
using a calculator.
Addition and subtraction
4Nc17
Add pairs of 3 digit numbers.
Use dice to generate 3 single digits.
Rearrange them to make 2 three digit
numbers and add. Repeat.
Numbered dice.
4Nc18
Subtract a 2 digit number from a 3
digit number.
Use dice to generate 3 single digits,
rearrange them to make one 2 digit
number and one 3 digit number.
Subtract the smaller from the larger.
Numbered dice.
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Mathematics Stage 4
4
Framework
Codes
Learning Objective
Activities
Resources
4Nc19
Subtract pairs of 3 digit numbers.
Use dice to generate 3 single digits,
rearrange them to make 2 three digit
numbers, Subtract one from the other.
Numbered dice.
Comments
Multiplication and division
4Nc20
Double any 2 digit number.
Go shopping: Twins go shopping and
they like to dress alike, and eat the
same food. Make a list of shopping for
one of the twins. If they both go
shopping, how much will be spent?
Sheets with clothing priced
and sheets of food items
priced.
Sheets need to be
prepared.
4Nc21
Multiply multiples of 10 to 90 by a
single digit number.
Groups of 3: chooser; operator;
guesser. Chooser picks a card from a
pack 1 -9 .and a card from a pack of
multiples of 10 (10 – 90) and shows
‘operator’ who calculates the answer
(using paper and pencil if necessary)
Guesser has to estimate the answer.
Discuss the outcomes. Change roles.
Number cards 1 – 9; number
cards, multiples of 10 (10 90);
Cards need to be
prepared.
4Nc22
Multiply a 2 digit number by a single
digit number.
Groups of 3 as above. Chooser picks a
card for a pack 1-9 and a card from a
pack of 2 digit numbers. Shows
operator who calculates the answer.
Guesser estimates the answer. Discuss
the outcomes. Change roles.
Number cards 1 -9, set of 2
digit numbers.
Cards need to be
prepared.
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Mathematics Stage 4
5
Framework
Codes
Learning Objective
Activities
Resources
4Nc23
Divide 2 digit numbers by single
digit numbers.
As above but using division.
Number cards appropriate to
the division facts.
4Nc25
Understand that the multiplication
and division are the inverse function
of each other.
Using multiplication and division sign
cards and a related set of number cards
ask students to make as many number
sentences as they can with just those
numbers and multiplication and division
symbols.
Multiplication and division sign
cards; related number cards.
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Mathematics Stage 4
Comments
6
Framework
Codes
Learning Objective
Activities
Resources
Comments
Problem Solving
Using techniques and skills in
solving mathematical problems.
4Pt1
Choose appropriate mental or
written strategies to carry out
calculations involving addition and
subtraction.
Use strategies when working in a
calculation lesson.
4Pt3
Check the results of adding
numbers by adding them in a
different order or by subtracting one
number from the total.
Use this strategy as one possible
during a calculation lesson.
4Pt4
Check subtraction by adding the
answer to the smaller number in the
original calculation.
Use this strategy as one possible
during a calculation lesson.
4Pt8
Estimate and approximate when
calculating and check working.
Using a calculator and 2 single digit
numbers, estimate the result of using
the 4 rules of number with those 2
numbers. Do the calculations on the
calculator. How close were the
estimates? Discuss differences.
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Mathematics Stage 4
Calculator; digit cards 1 – 9.
7
Framework
Codes
Learning Objective
Activities
Resources
Number dice; sign dice.
Comments
Using understanding and
strategies in solving problems
4Ps1
Make up a number story for a
calculation.
Use dice to generate numbers and a
sign dice to generate the operations.
4Ps2
Explain reasons for a choice of
strategy when multiplying or
dividing
.
Choose strategies to find answers
to addition or subtraction problems;
explain and show working.
Use during the last part of a lesson
involving multiplication or division.
4Ps4
Explore and solve number
problems and puzzles.
E.g. find 2 consecutive numbers with a
total of ??
Two consecutive numbers with a
product of ??
4Ps5
Use ordered lists and tables to help
solve problems systematically.
4Ps9
Explain methods and reasoning
orally and in writing.
Explain calculations that have been
completed or partly completed. Develop
the use of correct vocabulary to explain.
Make hypotheses and test them
out.
Make and justify decisions Explain
methods and reasoning.
4Ps3
V1 1Y07
Use during the main or last part of a
lesson involving addition and
subtraction problems.
Mathematics Stage 4
Calculators.
8
Scheme of Work – Mathematics stage 4
Unit 1B: Measure and Problem Solving
Framework
Codes
Learning Objective
Activities
Resources
Vocabulary cards of
abbreviations and the whole
word.
Comments
Measure
4Ml1
Choose and use standard metric
units and their abbreviations when
estimating, measuring and recording
length, weight and capacity.
Use correctly the abbreviations: mm
(millimetre), cm (centimetre), m (metre),
km (kilometre), g (gram), kg (kilogram),
ml (millilitre), l (litre), when answer
questions relating to measures.
4Ml2
Know and use the relationships
between familiar units of length,
mass and capacity, know the
meaning of kilo-, cent-, and milli-.
What would you use to measure … ?
Why? Would that be a sensible
measure to use? Why/why not?
4Ml4
Interpret intervals. Division on
partially numbered scales; record
readings accurately.
Choose a suitable measuring
instrument to measure for example:
A book, a table, the classroom
The weight of an apple, a bag of
apples, a person.
The capacity of a jug, a cup, a large
bottle. Interpret and record the
readings.
Measuring apparatus
4Mt1
Read and tell the time to the nearest
minute on 12 hour digital and
analogue clocks.
Use the vocabulary related to time.
Read the time to the minute on a 12
hour digital clock and on an analogue
clock. Know that 5.47 or 47 minutes
past 5 or 13 minutes to 6 are all
equivalent.
Analogue and digital clocks.
V1 1Y07
Mathematics Stage 4
Observations of
students working can
be used as an
assessment aid.
Use observation during
practical work as well
as questioning as an
assessment tool.
9
Framework
Codes
Learning Objective
Activities
Resources
4Mt2
Use AM, PM and 12 hour digital
clock notation.
4Mt3
Read simple timetables and use a
calendar.
Use a calendar to work out which day
of the week 26th April is; the date of the
second Wednesday in November; the
number of days from 30th June to 4th
August, and the number of weeks from
4th July to 30th October.
Use a T.V. guide to work out the length
of favourite programmes, use the class
timetable to find out how much time you
spend in a maths lesson every day,
every week.
Examples of calendars and
timetables.
4Mt4
Choose units of time to measure time
intervals.
Collect ideas to estimate or measure:
The time it takes to come to school;
The time it takes to get home;
The time you watch T.V. each week;
How long it is until the end of the year.
What measurement of time to:
Run a race; bake a cake; eat a meal?
Stop watches, sand timers,
analogue clocks with a second
hand, and digital clocks as
examples.
4Ma1
Draw rectangles and measure and
calculate their perimeters.
Use the vocabulary of area and
perimeter.
Respond to questions: Draw different
rectangles with a perimeter of 32 cm.
Which has the largest area?
The perimeter of a square is 24 cm.
What is the length of 1 side? Draw 2
rectangles with the same perimeter as
the square.
Rulers.
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Mathematics Stage 4
Comments
10
Framework
Codes
Learning Objective
Activities
Resources
4Ma2
Understand that area is measured in
square units e.g. cms squared.
Find areas by counting squares.
Centimetre square paper.
4Ma3
Find the area of rectilinear shapes
drawn on a square grid by counting
squares.
Using prepared sheets with shapes
drawn on cm square paper, ask ‘What
area is shaded? Find different ways of
halving the area of a 5 x 5 grid.
Centimetre square paper.
Prepared sheets.
V1 1Y07
Mathematics Stage 4
Comments
11
Framework
Codes
Learning Objective
Activities
Resources
Comments
Problem solving
4Pt2
Understand everyday systems of
measurement in length, weight and
capacity and time and use these to
solve simple problems as appropriate
What would you use to measure … ?
Why? Would that be a sensible
measure to use? Why/why not?
4Pt8
Estimate and approximate when
calculating, and check working
Estimate and check, using standard
units measurements such as:
How tall your teacher is; how heavy a
football is; how much a bucket holds;
how long/wide your table is.
4Ps1
Make up a number story for a
calculation, including in the context of
measures
Solve story problems and explain and
record how the problem was solved,
e.g. Measure the lengths of string
where not all are straight; change this
recipe for 5 people to a recipe for 10 (or
15)
4Ps9
Explain methods and reasoning
orally and in writing; make
hypotheses and test them out.
What would you use to measure … ?
Why? Would that be a sensible
measure to use? Why/why not?
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Mathematics Stage 4
12
Scheme of Work – Mathematics stage 4
Unit 1C: Handling Data and Problem Solving
Framework
Codes
Learning Objective
Activities
Resources
Comments
A collection of questions which
can be used as a basis of
collecting and handling data
Allow group and class
discussion of the
findings. Watch to see
which students find the
activity easy/difficult.
Use this as an
assessment
opportunity
Handling data
4Dh1
Answer a question by identifying
what data to collect, organising,
presenting and interpreting data in
tables, diagrams, tally charts,
frequency tables, pictograms and bar
charts.
Use, read and write vocabulary related
to data.
Find the answer to a question by
collecting data quickly then make a tally
chart. Discuss the findings.
Transfer the information to a different
type of graph or chart.
4Dh2
Compare the impact of
representations where scales have
different intervals.
Answer a question or solve a problem
by interpreting a bar chart or a
pictogram with the vertical axis marked
in multiples of 2. Using the same
information, mark the intervals in
multiples of 5 or 10 or 20? What
difference does it make to the
representation? Discuss as a class or a
group.
4Dh3
Use Venn or Carroll diagrams to sort
data and objects using 2 or 3 criteria.
Use sorting diagrams such as two-way
Venn and Carroll diagrams to show
information about shapes or numbers.
Change the shapes or numbers and
find new rules for sorting.
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Mathematics Stage 4
Prepared Venn or Carroll
diagrams.
13
Framework
Codes
Learning Objective
Activities
Resources
Comments
Problem solving
4Ps5
Use ordered lists and tables to help
to solve problems systematically.
Find the answer to a question by using
data collection in another subject or as
part of a homework activity. Discuss the
findings.
4Ps9
Explain methods and reasoning
orally and in writing; make
hypotheses and test them out.
Find the answer to a question by using
data collection in another subject or as
part of a homework activity. Discuss the
findings.
V1 1Y07
Mathematics Stage 4
14
Scheme of Work – Mathematics stage 4
Unit 2A: Number and Problem Solving
Framework
Codes
Learning Objective
Activities
Resources
Comments
Count on and back in ones, tens,
hundreds and thousands from four
digit numbers.
Class chanting and targeted questions.
Place value chart
1 2 3 4 5…
10 20 30 40 50 …
100 200 300 400 500 …
You may need to
spend some time
discussing the place
value chart.
4Nn3
Understand what each digit
represents in a three or four digit
number and partition into thousands,
hundreds, tens and units.
Use place value (arrow) cards.
Large set or teacher
modelling. Small set for table
top and ‘show me’ activities.
4Nn9
Round 3 and 4 digit numbers to the
nearest 10 or 100.
Give examples:
295 is 300 rounded to nearest 10
7402 is 7400 rounded to nearest 10
2743 is 2700 rounded to nearest
hundred.
4Nn7
Multiply and divide three-digit
numbers by 10 (whole number
answers) and understand the effect;
begin to multiply numbers by
100 and perform related divisions.
Put a number into the display, press x
10. What happens?
Try with a different start number. Try 2digit, 3-digit numbers. What happens?
Put a number in to the display, press /
10 What happens? What can you see?
Find a number where there is no
decimal point showing in the display.
What do you notice about those
numbers?
Numbers and the number system
4Nn2
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Mathematics Stage 4
Calculator.
Place value chart.
Make sure that
students are familiar
with how to use a
calculator.
15
Framework
Codes
Learning Objective
Activities
Resources
4Nn13
Use negative numbers in context,
e.g. temperature.
Use, read and write the vocabulary
associated with negative numbers
Recognise positive and negative whole
numbers (integers) in contexts such as
temperature, above ground and below
ground (a lift)…
Count back from any small number
through zero.
Place numbers on blank number line.
Number line to include
negative numbers.
Blank numbers lines with only
zero marked in the centre.
4Nn14
Recognise and extend number
sequences formed by counting in
steps of constant size, extending
beyond zero when counting back.
Count on and back:
From any 2-digit number count in steps
of 2, 3, 4, 5, 10.
Count back in 5s from 50
Describe, extend and explain number
sequences and patterns
Use knowledge of 2x timbale to work
out 4x table. Use 4x table to work out
8x table.
Number line.
Recognise odd and even numbers.
Give reasons why a number is odd or
even. 2-digit, 3-digit, 4-digit.
Make a general rule.
4Nn15
V1 1Y07
Mathematics Stage 4
Comments
Hundred square.
16
Framework
Codes
Learning Objective
Activities
Resources
4Nn16
Make general statements about the
sums and differences of odd and
even numbers.
Choose 2 even numbers and find their
total. Is the answer odd or even?
Choose 2 different even numbers and
repeat. Choose 3 or 4 digit even
numbers and repeat.
What do you notice?
What is the general statement you can
make about the total of even adding
even numbers?
Repeat with 2 odd numbers.
Repeat with 3 odd numbers. What
happens to the totals?
4Nn4
Use decimal notation and place
value for tenths and hundredths in
context, e.g. order amounts of
money; convert a sum of money
such as £13.25 to pence, or a length
such as 125 cm to metres; round a
sum of money to the nearest pound.
Using understanding of multiplying and
dividing by 10, (x a number by 10 digits
move 1 one place to the left, divide by
10, digits move 1 place to the right)
Explain the place value grid which
1 2 3 4 5…
10 20 30 40 50 …
100 200 300 400 500 …
Shows multiplication by 10. What
happens when you divide by 10?
Solve problems involving money,
explaining how the problem was solved.
Comments
Place value grid
Convert $ or € to cents and vice versa.
4Nn6
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Find multiples of 10, 100, 1000
more/less than numbers of up to four
digits, e.g. 3407 + 20 = 3427.
Use knowledge and understanding of
place value.
Use place value cards to change digits.
Mathematics Stage 4
Place value (arrow) cards.
17
Framework
Codes
Learning Objective
Activities
Resources
Comments
Calculation
Mental strategies
4Nc5
4Nc9
V1 1Y07
Recognise and begin to know
multiples of 2, 3, 4, 5 and 10 up to
the tenth multiple.
Add any pair of 2 digit numbers,
choosing an appropriate strategy.
Use 0 – 99 square as a visual model.
Place counter on zero and move it in
jumps of 2, then 3, then 4, then 5 and
10.
This gives an early opportunity to count
forwards and backwards in various
multiples with the help of the number
square. Students record the numbers in
a sequence and predict the next in the
sequence.
0 – 99 hundred square – 1 for
teacher demonstration, 1 each
for table top.
Counters.
Multiples charts.
For addition:
Look for pairs that make a multiple of
10 and do these first;
Start with the largest number
Partition and recombine (partition into
tens and units) Look for doubles and
near doubles.
Mathematics Stage 4
18
Framework
Codes
Learning Objective
4Nc10
Subtract any pair of 2 digit numbers,
choosing an appropriate strategy.
4Nc13
Multiply any pair of single digit
numbers together.
Use knowledge and understanding of
times tables.
Tables charts.
4Nc14
Use knowledge of commutativity to
find the easier way to multiply.
Understand that in multiplication the
commutative law is
3 x 25 = 25 x 3
Use what they know ( 7x3) to find what
they don’t know (3x7)
Become familiar with multiplication
square looking for patterns.
Multiplication square.
4Nc1
Derive quickly pairs of two-digit
numbers with a total of 100,
e.g. 72 + � = 100.
Use known number facts and place
value to add numbers with a total of
100.
Large place value cards for
teacher modelling.
Small place value cards for
table top.
V1 1Y07
Activities
Resources
Comments
Develop and recognise patterns:
11 – 3 = 8
21 – 13 = 8
31 – 23 = 8…..
100 – 29 could be done by:
Subtracting 30 and adding 1
Subtracting 20 then subtracting 9
Subtracting 29 from 99 and adding 1
Subtracting 28 from 99
Subtracting 30 from 101
Starting at 29, add 1 to make 30, add
70 to make 100
Or any way has student has of their
own.
Mathematics Stage 4
19
Framework
Codes
Learning Objective
Activities
4Nc2
Derive quickly pairs of multiples of 50
with a total of 1000,
e.g. 850 + � = 1000.
Use known number facts and place
value to add numbers with a total of
1000.
4Nc4
Know multiplication for 2×, 3×, 4×,
5×, 6×, 9× and 10× tables and derive
division facts.
Class chanting of tables with targeted
questions.
4 x 10 = 40, 40 divided by 10 = 4
Encourage looking for patterns in the
numbers.
4Nc7
Add three two-digit multiples of 10,
e.g. 40 + 70 + 50.
Use knowledge of addition to 10 and
adjust.
4Nc8
Add and subtract near multiples of
10 or 100 to or from three-digit
numbers, e.g. 367 – 198 or 278 + 49.
Keep in the horizontal format and
discuss strategies:
Round up or round down and adjust
Round to nearest 10 or 100 and adjust
Partition numbers to hundreds tens and
units (367 = 300 + 60 + 7)
Add hundreds first, then tens then units
and add all three totals together.
Students should be encouraged to
derive their own strategies.
Empty number line
4Nc11
Find a difference between near
multiples of 100, e.g. 304 – 296.
Round up or down and adjust.
Discuss other strategies. Encourage
students to find their own.
Empty number line
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Resources
Mathematics Stage 4
Comments
20
Framework
Codes
Learning Objective
Activities
Resources
4Nc12
Subtract a small number crossing
100, e.g. 304 – 8.
Discuss strategies:
Subtract 4 then 4 again.
Use an empty number line.
Encourage students to find strategies of
their own.
Empty number line
4Nc16
Derive quickly doubles of all whole
numbers to 50, doubles of multiples
of 10 to 500, doubles of multiples of
100 to 5000, and corresponding
halves.
Understand that doubling is the inverse
of halving (half of 20 is 10 therefore
double 10 is 20)
Doubling is x 2, halving is dividing by 2.
Comments
Addition and subtraction
4Nc17
V1 1Y07
Add pairs of 3 digit numbers.
Discuss strategies.
Look for pairs that make a multiple of
10 and do these first;
Start with the largest number
Look for doubles and near doubles.
Round up or round down and adjust
Round to nearest 10 or 100 and adjust
Partition numbers to hundreds tens and
units (367 = 300 + 60 + 7)
Add hundreds first, then tens then units
and add all three totals together
Students should be encouraged to
derive their own strategies.
Mathematics Stage 4
Empty number line
21
Framework
Codes
Learning Objective
Activities
Resources
4Nc18
Subtract a 2 digit number from a 3
digit number.
Keep in horizontal format and discuss
strategies.
Use knowledge of place value to
partition numbers.
Break numbers in to hundreds, tens
and units.
Give students opportunities to develop
their own strategies. Share them with
the rest of the class.
Empty number line
4Nc19
Subtract pairs of 3 digit numbers.
Keep in horizontal format and discuss
strategies.
Use knowledge of place value to
partition numbers.
Break numbers in to hundreds, tens
and units.
Give students opportunities to develop
their own strategies. Share them with
the rest of the class.
Empty number line
Discuss strategies.
Use knowledge and understanding of
place value.
Rounding and adjusting.
Repeated addition (more likelihood of
error).
Rules for multiplication (x tables).
Students share their own strategies.
Empty number line
Comments
Place value (arrow cards
Multiplication and division
4Nc22
V1 1Y07
Multiply a 2 digit number by a single
digit number.
Mathematics Stage 4
22
Framework
Codes
Learning Objective
Activities
4Nc24
Divide 2 digit numbers by single digit
numbers.
Use knowledge and understanding of
inverse operations (division is the
inverse of multiplication).
Discuss strategies.
4Nc24
Decide whether to round up or down
after division to give an answer to a
problem.
Make sensible decisions about whether
to round up or round down after division
For example:
Rounding up:
I have 52 eggs. One box holds 6 eggs. I
will need 9 boxes.
Rounding down:
I have 52 eggs. One box holds 6 eggs. I
could only fill 8 boxes.
V1 1Y07
Resources
Mathematics Stage 4
Comments
23
Framework
Codes
Learning Objective
Activities
Resources
Comments
Problem Solving
Using techniques and skills in solving
mathematical problems
4Pt1
Choose appropriate mental or written
strategies to carry out calculations
involving addition and subtraction.
Discuss strategies.
Look for pairs that make a multiple of
10 and do these first.
Start with the largest number.
Look for doubles and near doubles.
Round up or round down and adjust.
Round to nearest 10 or 100 and adjust.
Partition numbers to hundreds tens and
units (367 = 300 + 60 + 7).
Add hundreds first, then tens then units
and add all three totals together.
Students should be encouraged to
derive their own strategies.
4Pt3
Check the results of adding numbers
by adding them in a different order or
by subtracting one number from the
total.
Understand and use inverse
operations.
Check subtraction by adding the
answer to the smaller number in the
original calculation.
Understand and use inverse
operations.
4Pt4
Rearranging numbers to use different
strategies.
Rearranging numbers to use different
strategies
4Pt8
V1 1Y07
Estimate and approximate when
calculating and check working.
Explain how the estimate was made
and justify why it is reasonable.
Mathematics Stage 4
24
Framework
Codes
Learning Objective
Activities
Resources
4Pt5
Check multiplication using a different
technique, e.g. check
6 × 8 = 48 by doing 6 × 4 and
doubling.
Look for and devise different strategies.
4Pt6
Check the result of a division using
multiplication, e.g. multiply 4 by
12 to check 48 ÷ 4.
Use knowledge and understanding of
inverse operations.
Comments
Using understanding and
strategies in solving problems
4Ps1
Make up a number story for a
calculation.
What could the story be?
17 + 56 +34 = 107
68 – 56 +23 = 35
Make up more stories.
4Ps2
Explain reasons for a choice of
strategy when multiplying or dividing.
Discuss strategies and give reasons for
the choices made.
4Ps6
Describe and continue number
sequences, e.g. 7, 4, 1, –2 ...
identifying the relationship between
each number.
Look for patterns and connections.
Devise number sequences for others
to solve
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Mathematics Stage 4
25
Framework
Codes
Learning Objective
Activities
4Ps3
Choose strategies to find answers to
addition or subtraction problems;
explain and show working.
Discuss strategies.
Look for pairs that make a multiple of
10 and do these first;
Start with the largest number.
Look for doubles and near doubles.
Round up or round down and adjust.
Round to nearest 10 or 100 and adjust.
Partition numbers to hundreds tens and
units (367 = 300 + 60 + 7).
Add hundreds first, then tens then units
and add all three totals together.
Students should be encouraged to
derive their own strategies Discuss
strategies.
Use knowledge and understanding of
place value.
Rounding and adjusting.
Repeated addition (more likelihood of
error).
Rules for multiplication (x tables).
Use knowledge of place value to
partition numbers.
Break numbers in to hundreds, tens
and units.
4ps4
Explore and solve number problems
and puzzles.
Use a range of word problems, logic
problems, finding all possibilities,
diagram problems and visual problems,
finding rules and describing patterns.
Use ordered lists and tables to help
solve problems systematically.
Use within data handling and problem
solving.
V1 1Y07
Resources
Mathematics Stage 4
Comments
26
Framework
Codes
Learning Objective
Activities
Resources
4Ps9
Explain methods and reasoning
orally and in writing.
Bring into whole class, group and pair
working.
4Ps8
Investigate a simple general
statement by finding examples which
do or do not satisfy it.
I think a square is a rectangle. What do
you think?
Comments
If you multiply a number by 10 the
answer is always bigger than the start
number.
V1 1Y07
Mathematics Stage 4
27
Scheme of Work – Mathematics stage 4
Unit 2B: Geometry and Problem Solving
Framework
Codes
. 4Gs1
V1 1Y07
Learning Objective
Activities
Resources
Shapes and geometric reasoning
Use, read and write the vocabulary
relating to shape
Identify, describe, visualise, draw
and make a wider range of 2D and
3D shapes including a range of
quadrilaterals, the heptagon and
tetrahedron; use pin boards to create
a range of polygons. Use spotty
paper to record results.
2D: Know that a polygon is a closed flat
shape with 3 or more straight sides.
Ask class to draw as many polygons as
they can within 10 minutes. Share with
the rest of the group.
Regular polygons have all their sides
and angles equal. Ask the class to draw
as many regular polygons as possible
in 10 minutes. Share with the rest of the
group. Feedback to whole class the
different types.
Sort, name and classify. Put into a table
or list or use a Carroll diagram.
3D: Know that in a polyhedron each
face is a flat surface and is a polygon;
an edge is a straight line where 2 faces
meet; a vertex is the point where 3 or
more edges meet.
Know that a prism has 2 identical ends
and the same cross section throughout.
Collect, name and describe examples.
Mathematics Stage 4
Comments
Rulers
28
Framework
Codes
Learning Objective
Activities
4Gs2
Classify polygons (including a range
of quadrilaterals) using criteria
such as the number of right angles,
whether or not they are regular
and their symmetrical properties.
Know the angle and side properties of
isosceles, equilateral, scalene and right
angle triangles. Collect and draw
examples of each.
Name and classify polygons according
to their properties using a Carroll
diagram.
Identify particular shapes from a mixed
set.
4Gs3
Identify and sketch lines of symmetry
in 2D shapes and patterns.
Identify whether examples from real life
(fabric, wallpaper, logos,
advertisements, road signs ….) have a
line of symmetry.
Design a logo with a line of symmetry/2
lines of symmetry.
Make patterns by repeatedly reflecting
it.
4Gs4
Visualise 3D objects from 2D nets
and drawings and make nets of
common solids.
Identify simple nets of 3D shapes by
unfolding packets that are cubes or
cuboids.
Use these nets to construct some new
ones. Make larger/smaller nets.
Make polyhedral using straws to make
‘skeleton’ shapes. Cover the faces with
paper.
4Gs5
Find examples of shapes and
symmetry in the environment and in
art.
Design a maths trail around the
classroom, school, outdoors or wider
community identifying shapes with
symmetry. Write a ‘shape with
symmetry’ trail for others to follow.
V1 1Y07
Resources
Mathematics Stage 4
Comments
29
Framework
Codes
Learning Objective
Activities
Resources
Comments
Position and movement
4Gp1
Describe and identify the position of
a square on a grid of squares where
rows and columns are numbered
and/or lettered.
Begin to understand that 4,5 describes
a point found by starting from the 0,0
and moving 4 squares across and 5
squares up.
Recognise that 3,6 and 6,3 describe
different squares
Design a grid with instructions to get
from the start (own choice) to another
square. Ask the children to offer ideas
for the context (mice to a piece of
cheese, rocket to the moon, shopper to
the shop …..).
4Gp2
Know that angles are measured in
degrees and that one whole turn is
360° or four right angles; compare
and order angles less than 180°.
Make and measure clockwise and anticlockwise turns, describing them in
degrees. Use students to turn or find
other examples in the classroom of
things that turn (hands on a clock,
compass direction).
4Gp3
Devise the directions to give to follow
a given path.
Have a start point for 1 student to
stand. Rest of the class give directions
one at a time to get the student from
start to an agreed finish position. What
are the least number of instructions
needed?
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Mathematics Stage 4
30
Framework
Codes
Learning Objective
Activities
Resources
Comments
Using techniques and skills in
solving mathematical problems
4Pt7
Recognise the relationships between
2D shapes and identify the
differences and similarities between
3D shapes.
Link with 4 Gs1
Using understanding and
strategies in solving problems
4Ps7
Identify simple relationships between
shapes, e.g. these polygons
are all regular because ...
Make statements for the class to
explore and come to a decision about
whether it is true or not.
The number of lines of reflective
symmetry in a regular polygon is equal
to the number of sides of the polygon.
Is that always true? Are there any
exceptions? How do you know? What
did you do to find out?
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Mathematics Stage 4
31
Scheme of Work – Mathematics stage 4
Unit 2C: Measure and Problem Solving
Framework
Codes
Learning Objective
Activities
Resources
Comments
Measure
4Ml1
Choose and use standard metric
units and their abbreviations when
estimating, measuring and recording
length, weight and capacity.
Use, read and write the vocabulary
associated with measure.
Use correctly the abbreviations:
Mm (millimetre); cm (centimetre); m
(metre); km (kilometre);g (gram); kg
(kilogram); ml (millitre); l (litre) when
estimating, measuring and recording
length, weight and capacity.
Labels with abbreviations
matched to the metric units.
4Ml2
Know and use the relationships
between familiar units of length,
mass and capacity, know the
meaning of kilo-, cent-, and milli-.
Know the equivalent of one half, one
quarter and three quarters and one
tenth of 1km in m, 1m in cm, 1kg in g
and 1litre in ml.
Use practical activities with jugs and
beakers to show equivalence of
capacity(1 litre), moving to exploring
one half, one quarter and three
quarters.
Use practical activities tapes, metre
sticks and rulers to show equivalence of
linear measure (1 metre), moving to
exploring half, quarter and three
quarters.
Repeat for mass.
Measuring apparatus for
length, mass and capacity.
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Mathematics Stage 4
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Framework
Codes
Learning Objective
Activities
Resources
4Ml4
Interpret intervals. Division on
partially numbered scales; record
readings accurately.
Choose a suitable measuring
instrument to measure: the length of
your hand, round your head, your pace,
the classroom, the hall, the field …..;
The weight of your book; the weight of
your bag; the weight of your friend; the
weight of the heaviest movable thing in
your classroom.
The capacity of a beaker; the capacity
of a jug; the capacity of a bottle ……
Measuring apparatus for
length, mass and capacity
4Ml3
Where appropriate, use decimal
notation to record measurements,
e.g. 1.3 m, 0.6 kg, 1.2 l.
Record estimated and measured
lengths (m and cm), weights (kg and g)
and capacity (l and ml) in decimal form.
(Link with 4Ml4).
V1 1Y07
Mathematics Stage 4
Comments
33
Framework
Codes
Learning Objective
Activities
Resources
Comments
4Mt1
Read and tell the time to the nearest
minute on 12 hour digital and
analogue clocks.
Use word problems to give practice and
consolidation in reading and telling the
time:
What time is it now? In 25 minutes we
are going to have lunch. What time will
it be then?
Lunch takes 40 minutes. What time will
it finish?
I got up for school at 6.50. Breakfast
took 20 minutes; getting washed and
dressed took 18 minutes. What time
was I ready to leave for school?
Analogue and digital clocks
Putting time in the
context of real life
allows students to
make connections to
what is already
familiar. Ask them to
suggest some ideas of
their own.
Use cards that show times on both
analogue and digital clocks and cards
that have the time in words. Shuffle
both sets and place them face down on
a table. Take turns to turn over one
card from the top of each pack. If they
match say snap. First player to say it
wins the cards. Left over cards are
placed face up and players take turns
to choose 2 that match. The winner is
the player with most cards when all
have been taken.
Snap cards
Show the same time in
different ways: 3:45 or
15 minutes to 4 or45
minutes past 3.
4Mt2
V1 1Y07
Use AM, PM and 12 hour digital
clock notation.
Use am and pm
Link this with 4Mt1 and use am and pm
on the snap cards.
Mathematics Stage 4
34
Framework
Codes
Learning Objective
Activities
Resources
4Mt3
Read simple timetables and use a
calendar.
Using this year’s calendar ask:
Which day of the week is your birthday?
Which day of the week is your friend’s
birthday?
What is the date of the second Friday in
November?
How many days between your birthday
until your friend’s birthday?
How many weeks from the 3rd July to
18th September?
Calendars
Comments
Timetables
Encourage students to ask questions of
their own.
Use the class timetable to see how
much time you spend on each subject
in a day.
How much time a week? How much
time a term? How much time a year?
Use railway time tables or bus
timetables to plan a journey.
4Mt4
Choose units of time to measure
time intervals.
Suggest things or events that you
would measure in: hours, minutes,
seconds, days, weeks, months, years.
The time to eat lunch.
The time to wait before your birthday.
The time to wait until your friend’s
birthday.
The time to bake a cake.
The time to run round the field.
The time to walk home.
The time to drive to school.
Ask students for more ideas.
V1 1Y07
Mathematics Stage 4
35
Framework
Codes
Learning Objective
Activities
Resources
4Ma1
Draw rectangles and measure and
calculate their perimeters.
Discuss the meaning of perimeter.
Give students examples of rectangles.
‘Draw round your rectangle, keeping
your pencil on the edge. How far did
your pencil go? Measure the distance
and record’
Change rectangles between the group,
Are all the measurements the same for
each rectangle If there are any that are
very different, spend time discussing
the reasons why this could be. Allow
students to re-measure.
Allow students to draw their own
rectangles and pass them around the
group to be measured.
Drawn rectangles, enough
different ones for each
member of the group
4Ma2
Understand that area is measured in
square units e.g. cms squared.
Do all rectangles with the same
perimeter look the same? How many
different rectangles can be drawn with
the same perimeter?
Cm square paper
Rulers
4Ma3
Find the area of rectilinear shapes
drawn on a square grid by counting
squares.
Using square paper draw different
rectangles with the same perimeter to
find the one with the largest area
Using materials such as greetings
cards, books, rulers ….. draw round an
object onto cm square paper and find
the area by counting the squares inside
the perimeter.
Cm square paper
Rulers
Greetings cards, books …..
Comments
Which book/card has the greatest
area?
What else can you find which is
rectilinear where the area can be found
by drawing the perimeter?
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Mathematics Stage 4
36
Framework
Codes
Learning Objective
Activities
Resources
Comments
Problem solving
4Pt2
4Pt8
Understand everyday systems of
measurement in length, weight and
capacity and time and use these to
solve simple problems as
appropriate.
Solve ‘story’ problems involving length,
weight, capacity and time.
Estimate and approximate when
calculating, and check working.
Estimate and check:
the height of a friend
how much a bowl holds
how long the hall is
how fast you can run
how far you can jump
Discuss answers and allow students to
readjust if they want to.
What if a jug has 1 litre and you pour in
another half a litre, but quarter of a litre
spills out. How much is left? How do
you know?
Ask students to devise problems for the
rest of the class.
4Ps1
Make up a number story for a
calculation, including in the context
of measures.
Link with 4Pt2.
4Ps9
Explain methods and reasoning
orally and in writing; make
hypotheses and test them out.
This objective needs to be threaded in
to all of the others in Measure.
Use questions to develop students
thinking, skills, knowledge and
understanding.
V1 1Y07
Mathematics Stage 4
37
Scheme of Work – Mathematics stage 4
Unit 3A: Number and Problem Solving
Framework
Codes
Learning Objective
Activities
Resources
Comments
Put a number into the display, press x
10. What happens?
Try with a different start number. Try 2digit, 3-digit numbers. What happens?
Put a number in to the display, press /
10 What happens? What can you see?
Find a number where there is no
decimal point showing in the display.
What do you notice about those
numbers?
Put a number into the display. Press x
100. What do you notice? Try another
number. Does the same thing happen?
Put a number in the display. Press x
100. Record your start number and the
answer. Press /100. What do you
notice?
Calculator
Place value chart
Students need to know
how to use a calculator
and read the place
value chart
Numbers and the number system
4Nn7
V1 1Y07
Multiply and divide three-digit
numbers by 10 (whole number
answers) and understand the effect;
begin to multiply numbers by
100 and perform related divisions.
Mathematics Stage 4
38
Framework
Codes
Learning Objective
Activities
Resources
Comments
4Nn13
Use negative numbers in context,
e.g. temperature.
Use, read and write the vocabulary
associated with negative numbers
Recognise positive and negative whole
numbers (integers) in contexts such as
temperature, above ground and below
ground (a lift), …….
Count back from any small number
through zero.
Place numbers on blank number line
Use thermometers to take body
temperature, inside the classroom,
outside, Put temperatures in order,
lowest first.
Number line to include
negative numbers.
Blank numbers lines with only
zero marked in the centre.
Using real life contexts
can help students to
make connections.
4Nn14
Recognise and extend number
sequences formed by counting in
steps of constant size, extending
beyond zero when counting back.
Count on and back:
From any 2-digit number count in steps
of 2, 3, 4, 5, 10.
Count back in 5s from 50
Describe, extend and explain number
sequences and patterns.
Use knowledge of 2x timbale to work
out 4x table. Use 4 x table to work out
8x table.
Number line.
Recognise odd and even numbers.
Give reasons why a number is odd or
even. 2-digit, 3-digit, 4-digit.
Make a general rule.
4Nn15
Hundred square.
Extend to negative and decimal
numbers.
V1 1Y07
Mathematics Stage 4
39
Framework
Codes
Learning Objective
Activities
4Nn16
Make general statements about the
sums and differences of odd and
even numbers.
Choose 2 even numbers and find their
total. Is the answer odd or even?
Choose 2 different even number and
repeat. Choose 3 or 4 digit even
numbers and repeat.
What do you notice?
What is the general statement you can
make about the total of even adding
even numbers?
Repeat with 2 odd numbers.
Repeat with 3 odd numbers. What
happens to the totals?
Gather information from the rest of your
group.
Make a general statement about
addition of 2, or 3 odd numbers.
4Nn4
Use decimal notation and place
value for tenths and hundredths in
context, e.g. order amounts of
money; convert a sum of money
such
as £13.25 to pence, or a length such
as 125 cm to metres; round a sum of
money to the nearest pound.
Resources
Using understanding of multiplying and
dividing by 10, (x a number by 10 digits
move 1 one place to the left, divide by
10, digits move 1 place to the right)
Explain the place value grid which
1 2 3 4 5…
10 20 30 40 50 …
100 200 300 400 500 …
Shows multiplication by 10. What
happens when you divide by 10?
Solve problems involving money,
explaining how the problem was solved.
Comments
Encouraging students
to reason can develop
their thinking.
Place value grid
Convert pounds to pence (or $ to cents)
and vice versa.
Convert metres and cm to centimetres
and vice versa.
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Mathematics Stage 4
40
Framework
Codes
Learning Objective
Activities
Resources
4Nn6
Find multiples of 10, 100, 1000
more/less than numbers of up to four
digits, e.g. 3407 + 20 = 3427.
Use knowledge and understanding of
place value.
Use place value cards to change digits.
Place value (arrow) cards
4Nn17
Order and compare two or more
fractions with the same denominator
(halves, quarters, thirds, fifths,
eighths or tenths).
Revise the meaning of denominator
and numerator. Revise what each
stands for. Arrange fraction cards on a
number line/fraction line/blank number
line.
Which fraction is greater? How do you
know?
Empty number line
Fraction cards.
4Nn18
Recognise the equivalence between:
½; 4/8; and 5/10; ¼; 2/8; 1/5 and 2/10
Using a multiplication square look
across any 2 rows which are next to
each other. What do you notice?
2 4 6 8 10 12 14 16 …..
4 8 12 16 20 24 28 32
Read them as fractions. What do you
notice?
Is this true for any 2 rows?
Cut along the rows and place one
above another. Read from left to right.
Are they all equivalent fractions?
Multiplication square
V1 1Y07
Mathematics Stage 4
Comments
41
Framework
Codes
Learning Objective
Activities
Resources
4Nn19
Use equivalence to help order
fractions, e.g. 7/10 and 3/4
Use the multiples square. Remind
students about the notation and the tem
numerator and denominator. Cover up
all the multiples except the top 2 rows.
Look see and say about the top 2 rows.
(The numbers on the second row are
double those on the top row).Select a
pair of numbers to make a fraction.
What do you notice? Divide the
numerator by the denominator (0.5).
Repeat until all pairs have been used.
All have the decimal 0.5 after division.
Therefore they are all equivalent.
Use different rows and knowledge of
decimals to order fractions on an empty
number line
Empty number line
Give each pair of students a calculator
between them, a set of fraction cards
and a set of decimal cards. Place the
fractions cards face down on the table.
Take turns to turn over the top card and
using the calculator divide the
numerator by the denominator. Find the
decimal card that matches the fraction
card. Repeat until all of the cards have
been used.
Calculator
Pack of fraction cards 1/10 ….
10/
10
Decimal cards 0.1 … 1
4Nn20
Understand the equivalence between
one-place decimals and fractions in
tenths.
Comments
Multiples square
Calculator
Play snap matching decimal and
fractions
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Mathematics Stage 4
42
Framework
Codes
Learning Objective
Activities
Resources
4Nn21
Understand that ½ is equivalent to
0.5 and also to 5/10.
Use knowledge and understanding of
equivalent fractions and of using a
calculator to find equivalent decimals,
develop understanding that ½ is
equivalent to 0.5 and also to 5/10.
Calculators.
Place value cards with
decimal point.
4Nn22
Recognise the equivalence between
the decimal fraction and vulgar
fraction forms of halves, quarters,
tenths and hundredths.
Use knowledge and understanding of
use of calculator to convert vulgar
fractions to decimal fractions.
Calculators.
Place value cards with
decimal point.
4Nn23
Recognise mixed numbers, e.g. 5 ¾
and order these on a number line
Recognise that 5¾ is more than 5 but
less than 6.
Recognise that 5¾ is more than 5½.
Recognise that 5¼ is more than 5 but
less than 5½
Number line
4Nn24
Relate finding fractions to division.
Understand that finding ½ is the same
as dividing by 2.
Recognise that when 1 pizza is divided
equally into 4, each person gets ¼
Calculator
4Nn25
Find halves, quarters, thirds, fifths,
eighths and tenths of shapes and
numbers.
Recognise that shapes have to be
divided into the same number of equal
parts as the denominator. Recognise
that the numerator refers to the number
of parts out of the whole.
Understand that finding one eighth is
equivalent to dividing by 8, so 1/8 of 24
is 3.
Calculator
V1 1Y07
Mathematics Stage 4
Comments
Regular shapes
43
Framework
Codes
Learning Objective
Activities
Resources
Comments
Calculation
Mental strategies
4Nc1
Derive quickly pairs of two-digit
numbers with a total of 100,
e.g. 72 + � = 100.
Use known number facts and place
value to add numbers with a total of
100.
4Nc2
Derive quickly pairs of multiples of 50
with a total of 1000,
e.g. 850 + � = 1000
Use known number facts and place
value to add numbers with a total of
1000.
4Nc4
Know multiplication for 2×, 3×, 4×,
5×, 6×, 9× and 10× tables and
derive division facts.
Class chanting of tables with targeted
questions
4 x 10 = 40, 40 divided by 10 = 4
Encourage looking for patterns in the
numbers
4Nc3
Identify simple fractions with a total
of 1, e.g. 4
1 + � = 1.
Addition and subtraction
4Nc7
V1 1Y07
Add three two-digit multiples of 10,
e.g. 40 + 70 + 50.
Use knowledge of addition to 10 and
adjust.
Mathematics Stage 4
44
Framework
Codes
Learning Objective
Activities
4Nc8
Add and subtract near multiples of
10 or 100 to or from three-digit
numbers, e.g. 367 – 198 or 278 + 49.
Keep in the horizontal format and
discuss strategies:
Round up or round down and adjust
Round to nearest 10 or 100 and adjust
Partition numbers to hundreds tens and
units (367 = 300 + 60 + 7)
Add hundreds first, then tens then units
and add all three totals together
Students should be encouraged to
derive their own strategies.
4Nc11
Find a difference between near
multiples of 100, e.g. 304 – 296.
Round up or down and adjust.
Discuss other strategies. Encourage
students to find their own.
4Nc12
Subtract a small number crossing
100, e.g. 304 – 8.
Discuss strategies:
Subtract 4 then 4 again.
Use an empty number line
Encourage students to find strategies of
their own.
4Nc16
Derive quickly doubles of all whole
numbers to 50, doubles of
multiples of 10 to 500, doubles of
multiples of 100 to 5000, and
corresponding halves.
Understand that doubling is the inverse
of halving (half of 20 is 10 therefore
double 10 is 20).
Doubling is x 2, halving is dividing by 2.
V1 1Y07
Resources
Mathematics Stage 4
Comments
45
Framework
Codes
Learning Objective
Activities
Resources
Comments
Multiplication and division
4Nc24
Decide whether to round up or down
after division to give an answer to a
problem.
4Nc26
Begin to understand simple ideas of
ratio and proportion, e.g. a picture is
one fifth the size of the real dog. It is
25 cm long in the picture, so it is 5 ×
25 cm long in real life.
V1 1Y07
Make sensible decisions about whether
to round up or round down after division
Revise the problem from before. For
example:
Rounding up:
I have 153 flowers. One box holds 50
flowers. I will need 4 boxes.
Rounding down:
I have 153 flowers. One box holds 50
flowers. I could only fill 3 boxes.
Set new problems and ask students to
make problems of their own.
Mathematics Stage 4
46
Framework
Codes
Learning Objective
Activities
Resources
Comments
Problem Solving
Using techniques and skills in solving
mathematical problems
4Pt1
Choose appropriate mental or written
strategies to carry out calculations
involving addition and subtraction.
Discuss strategies
Look for pairs that make a multiple of
10 and do these first;
Start with the largest number
Look for doubles and near doubles.
Round up or round down and adjust
Round to nearest 10 or 100 and adjust
Partition numbers to hundreds tens and
units (367 = 300 + 60 + 7)
Add hundreds first, then tens then units
and add all three totals together.
Students should be encouraged to
derive their own strategies.
4Pt3
Check the results of adding numbers
by adding them in a different order or
by subtracting one number from the
total.
Understand and use inverse operations
Check subtraction by adding the
answer to the smaller number in the
original calculation.
Understand and use inverse
operations.
4Pt4
Rearranging numbers to use different
strategies.
Rearranging numbers to use different
strategies.
4Pt8
V1 1Y07
Estimate and approximate when
calculating and check working.
Explain how the estimate was made
and justify why it is reasonable.
Mathematics Stage 4
47
Framework
Codes
Learning Objective
Activities
Resources
4Pt5
Check multiplication using a different
technique, e.g. check
6 × 8 = 48 by doing 6 × 4 and
doubling.
Look for and devise different strategies.
4Pt6
Check the result of a division using
multiplication, e.g. multiply 4 by
12 to check 48 ÷ 4.
Use knowledge and understanding of
inverse operations.
Comments
Using understanding and
strategies in solving problems
4Ps1
Make up a number story for a
calculation.
What could the story be?
43 – 67 = -24
17 divided by 2 = 8 remainder 1
Make up more stories
4Ps2
Explain reasons for a choice of
strategy when multiplying or dividing.
Discuss strategies and give reasons for
the choices made.
4Ps6
Describe and continue number
sequences, e.g. 7, 4, 1, –2 ...
identifying the relationship between
each number.
Look for patterns and connections.
Devise number sequences for others to
solve.
V1 1Y07
Mathematics Stage 4
48
Framework
Codes
Learning Objective
Activities
4Ps3
Choose strategies to find answers to
addition or subtraction problems;
explain and show working.
Discuss strategies
Look for pairs that make a multiple of
10 and do these first;
Start with the largest number
Look for doubles and near doubles.
Round up or round down and adjust
Round to nearest 10 or 100 and adjust
Partition numbers to hundreds tens and
units (367 = 300 + 60 + 7)
Add hundreds first, then tens then units
and add all three totals together
Students should be encouraged to
derive their own strategies Discuss
strategies
Use knowledge and understanding of
place value.
Rounding and adjusting
Repeated addition (more likelihood of
error)
Rules for multiplication (x tables).
Use knowledge of place value to
partition numbers.
Break numbers in to hundreds, tens
and units.
4Ps4
Explore and solve number problems
and puzzles.
Use a range of word problems, logic
problems, finding all possibilities,
diagram problems and visual problems,
finding rules and describing patterns.
4Ps5
Use ordered lists and tables to help
solve problems systematically.
Use within data handling and problem
solving.
V1 1Y07
Resources
Mathematics Stage 4
Comments
49
Framework
Codes
Learning Objective
Activities
Resources
4Ps9
Explain methods and reasoning
orally and in writing.
Bring into whole class, group and pair
working.
4Ps8
Investigate a simple general
statement by finding examples which
do or do not satisfy it.
For example:
The lines of symmetry on a regular
shape match the number of sides.
Comments
If you multiply a number by 10 the
decimal point moves to the left.
V1 1Y07
Mathematics Stage 4
50
Scheme of Work – Mathematics stage 4
Unit 3B: Measure and Problem Solving
Framework
Codes
Learning Objective
Activities
Measure
Many of these activities will revise and
consolidate the previous unit on
Measure.
4Ml1
Choose and use standard metric
units and their abbreviations when
estimating, measuring and
recording length, weight and
capacity.
4Ml2
Know and use the relationships
between familiar units of length,
mass and capacity, know the
meaning of kilo-, cent-, and milli-.
V1 1Y07
Resources
Comments
Use, read and write the vocabulary
associated with measure.
Use correctly the abbreviations:
Mm (millimetre); cm (centimetre); m
(metre); km (kilometre);g (gram); kg
(kilogram); ml (millitre); l (litre) when
estimating, measuring and recording
length, weight and capacity
Labels with abbreviations
matched to the metric units.
Add illustrations to the
labels for those
students who may find
reading difficult. This
will help them to make
connections.
Know the equivalent of one half, one
quarter and three quarters and one
tenth of 1km in m, 1m in cm, 1kg in g
and 1litre in ml.
Use practical activities with jugs and
beakers to show equivalence of
capacity (1 litre), moving to exploring
one half, one quarter and three
quarters.
Use practical activities tapes, metre
sticks and rulers to show equivalence of
linear measure (1 metre), moving to
exploring half, quarter and three
quarters.
Repeat for mass.
Measuring apparatus for
length, mass and capacity.
Making the activity
practical will
particularly help those
students who find
working in the abstract
difficult.
Mathematics Stage 4
51
Framework
Codes
Learning Objective
Activities
Resources
Comments
4Ml4
Interpret intervals. Division on
partially numbered scales; record
readings accurately.
Choose a suitable measuring
instrument to measure: the length of
your smallest finger, round a football,
your footstep, the corridor, the hall, the
field, your bedroom …..;
The weight of more than 1 book. What
happens if you change the books?; the
weight of your shoes. Do all pairs of
shoes weigh the same?; the weight of
your friend; the weight of you and your
friend. the weight of the lightest thing in
your classroom. Has anyone found
anything lighter?
The capacity of a beaker; the capacity
of a jug; the capacity of a bottle …..,
Measuring apparatus for
length, mass and capacity.
These ideas are best
done practically to help
students develop their
knowledge, skills and
understanding.
4Ml3
Where appropriate, use decimal
notation to record measurements,
e.g. 1.3 m, 0.6 kg, 1.2 l.
Record estimated and measured
lengths (m and cm), weights (kg and g)
and capacity (l and ml) in decimal form.
(Link with 4Ml4).
4Mt1
Read and tell the time to the
nearest minute on 12 hour digital
and analogue clocks.
Use word problems to give practice and
consolidation in reading and telling the
time:
What time is it now? In 13 minutes we
are going to have lunch. What time will
it be then?
I can eat my lunch in 21 minutes. What
time will I finish?
I got up for school at 15 minutes to 7.
Breakfast took 20 minutes; getting
washed and dressed took 18 minutes.
What time was I ready to leave for
school?
Analogue and digital clocks.
Break word problems
into smaller units for
some students.
V1 1Y07
Mathematics Stage 4
52
Framework
Codes
Learning Objective
Activities
Resources
Use cards that show times on both
analogue and digital clocks and cards
that have the time in words.
Snap cards.
Comments
Shuffle both sets and place them face
down on a table. Take turns to turn over
one card from the top of each pack. If
they match say snap. First player to say
it wins the cards. Left over cards are
placed face up and players take turns
to choose 2 that match. The winner is
the player with most cards when all
have been taken.
4Mt2
Use AM, PM and 12 hour digital
clock notation.
Link this with 4Mt1 and use am and pm
on the snap cards.
4Mt3
Read simple timetables and use a
calendar.
Using this year’s calendar ask:
Which day of the week did we start
school?
Which day of the week will we finish
school this term?
What is the date of the second Tuesday
in March?
How many days between starting
school this term and ending school?
How many weeks?
How many days from the 15th May to
26th April next year?
Calendars.
Timetables.
Encourage students to ask questions of
their own.
V1 1Y07
Mathematics Stage 4
53
Framework
Codes
Learning Objective
Activities
Resources
4Mt4
Choose units of time to measure
time intervals.
Use a different class timetable to see
how much time they spend on each
subject in a day.
How much time a week? How much
time a term? How much time a year?
Comments
Use railway time tables or bus
timetables or flight times to plan a
journey.
Suggest things or events that you
would measure in: hours, minutes,
seconds, days, weeks, months, years.
The time to eat lunch.
The time to wait before your birthday.
The time to wait until your friend’s
birthday.
The time to bake a cake.
The time to run round the field.
The time to walk home.
The time to drive to school.
Ask students for more ideas.
V1 1Y07
Mathematics Stage 4
54
Framework
Codes
Learning Objective
Activities
Resources
4Ma1
Draw rectangles and measure and
calculate their perimeters.
Discuss the meaning of perimeter.
Give students examples of rectangles.
‘Draw round your rectangle, keeping
your pencil on the edge. How far did
your pencil go? Measure the distance
and record’
Change rectangles between the group,
Are all the measurements the same for
each rectangle If there are any that are
very different, spend time discussing
the reasons why this could be. Allow
students to re-measure.
Allow students to draw their own
rectangles and pass them around the
group to be measured.
Drawn rectangles, enough
different ones for each
member of the group.
4Ma2
Understand that area is measured
in square units e.g. cms squared.
Do all rectangles with the same
perimeter look the same? How many
different rectangles can be drawn with
the same perimeter?
What length of sides will give the
largest area?
Cm square paper.
Rulers.
V1 1Y07
Mathematics Stage 4
Comments
55
Framework
Codes
Learning Objective
Activities
Resources
4Ma3
Find the area of rectilinear shapes
drawn on a square grid by counting
squares.
Using square paper draw different
rectangles with the same perimeter to
find the one with the largest area
Cm square paper.
Rulers.
Greetings cards, books.
Comments
Using materials such as greetings
cards, books, rulers ….. draw round an
object onto cm square paper and find
the area by counting the squares inside
the perimeter.
Find a book that gives the
largest/smallest area. Has anyone else
found a larger/smaller area than yours?
What other rectangles can you find?
Measure the perimeter and area.
V1 1Y07
Mathematics Stage 4
56
Framework
Codes
Learning Objective
Activities
Resources
Comments
Problem solving
Understand everyday systems of
measurement in length, weight and
capacity and time and use these to
solve simple problems as
appropriate.
Solve ‘story’ problems involving length,
weight, capacity and time.
4Pt8
Estimate and approximate when
calculating, and check working.
Estimate and check
the height of your teacher:
how much a bowl holds
how long the classroom is
how fast your friend can run 100 metres
how far your friend can jump
4Ps1
Make up a number story for a
calculation, including in the context
of measures.
What if a jug has half a litre and you
pour in another half a litre, but you spill
three quarters of a litre. How much is
left? How do you know?
Ask students to devise problems for the
rest of the class.
4Ps9
Explain methods and reasoning
orally and in writing; make
hypotheses and test them out.
Link with 4Pt2
4Pt2
V1 1Y07
Discuss answers and allow students to
readjust if they want to.
Mathematics Stage 4
57
Scheme of Work – Mathematics stage 4
Unit 3C: Handling Data and Problem solving
Framework
Codes
Learning Objective
Activities
Resources
Comments
Handling data
4Dh1
Answer a question by identifying
what data to collect, organising,
presenting and interpreting data in
tables, diagrams, tally charts,
frequency tables, pictograms and bar
charts.
Set problems or puzzles that involves
collecting data. Link with student
interest and events in the school or
wider community:
Use a tally chart for data that can be
collected quickly ‘Where would you like
to visit?’ Discuss the findings
Make a pictogram, where the symbol
represents several units ‘I think that ice
cream is our favourite dessert. How
could we find out?’ Discuss strategies
and then the findings
Using student interest
may generate more
discussion. Encourage
them to question and
debate the relative
merits of each type of
representation of data.
When is it better to use
one rather than
another? Does it
matter? Why?
Ask a question or solve a problem by
interpreting a bar chart or frequency
table.
‘What can you tell me about the
temperature of the water in the bath?
Why could this be?’
V1 1Y07
Mathematics Stage 4
58
Framework
Codes
Learning Objective
Activities
4Dh2
Compare the impact of
representations where scales have
different intervals.
Represent the same information on
block graphs where the scales have
different intervals. What do you notice?
Has anything changed? Why do you
think that is? Which shows us what we
want to know more effectively? What if
we changed the scale intervals again?
Would it be better or worse? Why?
4Dh3
Use Venn or Carroll diagrams to sort
data and objects using 2 or 3 criteria.
Use sorting diagrams such as Venn
and Carroll diagrams to display
information (shapes, numbers, sorting
resources …..)
Ask students to offer their own ideas.
V1 1Y07
Resources
Mathematics Stage 4
Comments
59
Framework
Codes
Learning Objective
Activities
Resources
Comments
Problem solving
4Ps5
Use ordered lists and tables to help
to solve problems systematically.
Link with 4Dh1. Use for data that can
be collected quickly in the first instance,
then use for more sustained
investigations. Discuss how important
being systematic is when dealing with
data.
4Ps4
Explain methods and reasoning
orally and in writing; make
hypotheses and test them out.
Integrate this with all aspects of
handling data.
V1 1Y07
Mathematics Stage 4
Encourage students to
discuss their methods
of data collection, their
findings and their
representations. Pair
or small group would
work well for this,
followed by whole
class discussion.
60